Tic-tac-toe is a paper-and-pencil game for two players, $X$ and $O$, who take turns marking the spaces in a $3 \times 3 $ grid.
Questions tagged [tic-tac-toe]
51 questions
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A non-losing strategy for tic-tac-toe $\times$ tic-tac-toe
Consider a $9 \times 9$ matrix that consists of $9$ block matrices of $3 \times 3$. Let each $3 \times 3$ block be a game of tic-tac-toe. For each game, label the $9$ cells of the game from $1$ to $9$ with order from left to right, from above to…
mez
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Is the aim of this Tic-Tac-Toe puzzle possible to achieve?
I was playing Tic-Tac-Toe with my friend when I came up with a puzzle. I might have to put this on the Puzzling Stack Exchange , but I do not know if the aim of the puzzle can be achieved. I am aware that math(s) is incorporated, so that is why I am…
Mr Pie
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Bidding Tic Tac Toe
In regular tic tac toe, both the players get alternate chances. This is a variant of that. Player $A$ has $\$x$ amount and player $B$ has $\$y$ amount as initial balance. Assume that $y>x$. Both the players bid some amount from the available amount…
Nimit
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Winning strategies in multidimensional tic-tac-toe
This question is a result of having too much free time years ago during military service. One of the many pastimes was playing tic-tac-toe in varying grid sizes and dimensions, and it lead me to a conjecture. Now, after several years of mathematical…
Joonas Ilmavirta
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Prove that a game of Tic-Tac-Toe played on the torus can never end in a draw. (Graph theoretic solutions only.)
Here's a problem I assigned to my graph theory class. The only caveat is that I insisted that their solutions be entirely graph theoretic. Have fun with it. Prove that a game of Tic-Tac-Toe played on the torus can never end in a draw. The idea is to…
Doc
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Prove that $5 \times 5 \times 5$ tic-tac-toe ends in a draw
I am pretty sure that when played perfectly, $5 \times 5 \times 5$ tic-tac-toe will end in a draw. Is anyone able to prove this?
suomynonA
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Tic-Tac-Toe on the Real Projective Plane is a trivial first-player win in three moves
Consider a $3 \times 3$ Tic-Tac-Toe board with opposite sides identified in opposite orientation. We play Tic-Tac-Toe in the Real Projective Plane. More precisely, consider a $3 \times 3$ Tic-Tac-Toe board on the unit square $[0,1]^2$ . We glue the…
Desura
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1 answer
Optimal Tic Tac Toe algorithm without lookahead
Is there any algorithm for tic tac toe that does not rely on a lookahead algorithm that is perfect for any sized boards? Edit: For boards larger than $3 \times 3$, we have to find the best move for a $k$ in a row where $k < n$ and we have a $n…
picakhu
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What are the symmetries of a tic tac toe game board?
What are the symmetries of the tic tac toe board game? In other words, what are the ways you can rotate, reflect, and/or flip the tic tac toe board, such that the next best move to a board (before it was rotated, reflected, etc) is still the next…
Jeff
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Probability of draw with random play on $N\times N$ Tic Tac Toe
I was coding a tic tac toe game where $2$ players play tic tac toe randomly on a given $N$ board size $(N\times N)$ . $X$ starts first. If one side gets $N$ consecutive (horizontal/vertical/diagonal) of their symbols, they win. If no one won and…
Minot
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Tic Tac Toe on an infinite grid
Imagine playing tic tac toe, but rather than the standard 3 by 3 grid, the board extends indefinitely in every direction. When playing the usual game, one player must get three squares in a row to wind the game. However, with an infinite grid, three…
PiGuy314
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Two players put fill $1$ and $0$ in a $3\times 3$ matrix and compute its determinant when it is full. Can Player $0$ win if $1$ starts at the center?
In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 × 3 matrix. Player 0 counters with a 0 in a vacant position, and play continues in turn until the 3 × 3 matrix is completed with five 1’s and four 0’s. Player 0 wins if the determinant is…
global05
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Why does the strategy-stealing argument for tic-tac-toe work?
On the Wikipedia page for strategy-stealing arguments , there is an example of such an argument applied to tic-tac-toe: A strategy-stealing argument for tic-tac-toe goes like this: suppose that the second player has a guaranteed winning strategy,…
templatetypedef
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Game combinations of tic-tac-toe
How many combinations are possible in the game tic-tac-toe ( Noughts and crosses )? So for example a game which looked like: (with positions 1-9) A1 -- B1 A2 -- B2 A3 -- -- [1][3][4][6][7] would be one combination
Danield
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1 answer
Optimal strategy for tic-tac-toe-like game "Otrio"
The game "Otrio" is sort of a 3D version of tic-tac-toe (2 space dimensions and 1 size). You play as 1 color on a 3x3 board, and you control 9 pieces (3 small, 3 medium, 3 large circles): There are 3 win conditions (paraphrasing from link below) :…
sambajetson
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